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Semiclassical Analysis of Dispersion Phenomena

  • Victor Chabu
  • Clotilde Fermanian-KammererEmail author
  • Fabricio Macià
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)

Abstract

Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schrödinger-type equation in \(\mathbf{R}^d\). We describe quantitatively the localisation of the energy in a long-time semiclassical limit within this non compact geometry and exhibit conditions under which the energy remains localized on compact sets. We also explain how our results can be applied in a straightforward way to describe obstructions to the validity of smoothing type estimates.

Keywords

Semiclassical analysis Schrödinger equations Wigner measures Degenerate critical points 

Notes

Acknowledgements

F. Macià has been supported by grants StG-2777778 (U.E.) and MTM2013-41780-P, TRA2013-41096-P (MINECO, Spain). Part of this work was done while V. Chabu was visiting ETSI Navales at Universidad Politécnica de Madrid in the fall of 2015. V. Chabu was partly supported by grant 2017/13865-0, São Paulo Research Foundation (FAPESP)

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Victor Chabu
    • 1
  • Clotilde Fermanian-Kammerer
    • 2
    Email author
  • Fabricio Macià
    • 3
  1. 1.Universidade de São Paulo, IF-USP, DFMA, CP 66.318São PauloBrazil
  2. 2.LAMA, UMR CNRS 8050, Université Paris EstCréteil CedexFrance
  3. 3.Universidad Politécnica de Madrid, DCAIN, ETSI NavalesMadridSpain

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